基于足底压力的人体重心轨迹包络面积算法
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摘要
为了评估人体平衡功能,需要计算人体重心轨迹包络曲线的面积,提出了一种包络曲线的计算方法。首先,通过足底压力采集系统获取足底压力数据,计算得到人体重心点;然后,提出了一种基于斜率逐步比较的重心轨迹包络凸多边形构造法,通过斜率比较筛选出包络凸多边形的顶点;最后,根据斜率大小对凸点进行排序,通过三角形面积累加得到包络凸多边形的面积。计算实例证明,提出的算法与经典的快包法相比提高了人体重心轨迹包络曲线面积的计算速度,算法具有良好的稳定性,稳定性差值在±0.01 s之内,算法的时间复杂度为O(nlgn),可有效应用于人体重心轨迹包络面积的计算。
In order to assess the human body balance function,a method of calculating the area of the envelope curve of the body barycenter is proposed. First,calculating the body barycenter use the plantar pressure acquisition system. Then,a convex polygon construction method was presented based on the slope of body barycenter,the vertex of the convex polygon was selected by slope comparison. Finally,the vertices are sorted according to the slope size,and the area of the convex polygons is obtained by accumulating the triangular area. The calculation example proves that the proposed algorithm improves the calculate speed of the envelope curve area of the body barycenter curve compared with the classical fast convex hull wrapping method. The algorithm has good stability,the difference in stability is within ± 0. 01 s. The time complexity of the algorithm is O( nlgn),effectively applied to the calculation of the envelope area of body barycenter.
In order to assess the human body balance function,a method of calculating the area of the envelope curve of the body barycenter is proposed. First,calculating the body barycenter use the plantar pressure acquisition system. Then,a convex polygon construction method was presented based on the slope of body barycenter,the vertex of the convex polygon was selected by slope comparison. Finally,the vertices are sorted according to the slope size,and the area of the convex polygons is obtained by accumulating the triangular area. The calculation example proves that the proposed algorithm improves the calculate speed of the envelope curve area of the body barycenter curve compared with the classical fast convex hull wrapping method. The algorithm has good stability,the difference in stability is within ± 0. 01 s. The time complexity of the algorithm is O( nlgn),effectively applied to the calculation of the envelope area of body barycenter.
引文
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3王红梅,徐秀林.人体动静态姿势平衡能力测试的理论与应用.中国组织工程研究与临床康复,2010;(43):8095-8098Wang Hongmei,Xu Xiulin.Theory and application of body balance function assessment.Journal of Clinical Rehabilitative Tissue Engineering Research,2010;14(43):8095-8098
4 Ye Q Z.A fast algorithm for convex-hull extraction in 2D images.Pattern Recognition Letters,1995;16(5):531-537
5 Hu K N,Yin L J.Multi-Scale topological features for hand posture representation and analysis.The Proceeding of International Conference on Computer Vision.New York:IEEE,2013:1928-1935
6 Yan M.Extension of convex function.Journal of Convex Analysis,2014;21(4):965-987
7蔡慧英,朱枫.仿射变换下基于凸包和多尺度积分特征的形状匹配方法.计算机辅助设计与图形学学报,2017;29(2):269-278Cai Huiying,Zhu Feng.Shape matching method based on convex hull and muitiscale integral features under affine transformation.Journal of Computer-aided Design&Computer Graphics,2017;29(2):269-278
8 Gomes A J P.A total order heuristic-based convex hull algorithm for points in the plane.Computer-Aided Design,2016;70:153-160
9 Cinque L,Di Maggio C.A BSP realisation of jarvis’algorithm.Pattern Recognition Letters,2001;22(2):147-155
10 Cormen T H,Charles E Leiserson,Ronald L Rivest,et al.Introduction to algrithms.Vol.2.Cambridge:MIT press,2001
11 Barber C B,Dobkin D P,Huhdanpaa H.The quickhull algorithm for convex hulls.ACM Transactions on Mathematical Software,1996;22(4):469-483
12 Chen M,Fang Y,Chen J.Influence of initial convex hull on the efficiency of quickhull algorithm.Science of Surveying and Mapping,2016;41(7):23-27
13 Anderson K R.Re-evaluation of an efficient algorithm for determining convex hull of a finite planar set.Information Processing Letters,1978;7(1):53-55
14 Gomes A J P.A total order heuristic-based convex hull algorithm for points in the plane.Computer-aided Design,2016;70:153-160
15刘崇,任立峰,史建伟,等.人体平衡能力的评价系统.中国组织工程研究与临床康复,2009;13(2):363-367Liu Chong,Ren Lifeng,Shi Jianwei,et al.Evaluation system of human balance ability.Journal of Clinical Rehabilitative Tissue Engineering Research,2009;13(2):363-367
16安美君,邹任玲,胡秀坊,等.人体重心动摇轨迹包络面积的快速算法.计算机工程,2011;37(10):255-256An Meijun,Zhou Renlin,Hu Xiufang,et al.Fast algorithm for envelope area of body barycenter swaying trajectory.Computer Engineering,2011;37(10):255-256
17 Andrew C C Yao.A Lower Bound to Finding Convex Hulls.Journal of the ACM,1981;28(4):780-787
2 Horak F B.Clinical assessment of balance disorders.Gait&Posture,1997;6(1):76-84
3王红梅,徐秀林.人体动静态姿势平衡能力测试的理论与应用.中国组织工程研究与临床康复,2010;(43):8095-8098Wang Hongmei,Xu Xiulin.Theory and application of body balance function assessment.Journal of Clinical Rehabilitative Tissue Engineering Research,2010;14(43):8095-8098
4 Ye Q Z.A fast algorithm for convex-hull extraction in 2D images.Pattern Recognition Letters,1995;16(5):531-537
5 Hu K N,Yin L J.Multi-Scale topological features for hand posture representation and analysis.The Proceeding of International Conference on Computer Vision.New York:IEEE,2013:1928-1935
6 Yan M.Extension of convex function.Journal of Convex Analysis,2014;21(4):965-987
7蔡慧英,朱枫.仿射变换下基于凸包和多尺度积分特征的形状匹配方法.计算机辅助设计与图形学学报,2017;29(2):269-278Cai Huiying,Zhu Feng.Shape matching method based on convex hull and muitiscale integral features under affine transformation.Journal of Computer-aided Design&Computer Graphics,2017;29(2):269-278
8 Gomes A J P.A total order heuristic-based convex hull algorithm for points in the plane.Computer-Aided Design,2016;70:153-160
9 Cinque L,Di Maggio C.A BSP realisation of jarvis’algorithm.Pattern Recognition Letters,2001;22(2):147-155
10 Cormen T H,Charles E Leiserson,Ronald L Rivest,et al.Introduction to algrithms.Vol.2.Cambridge:MIT press,2001
11 Barber C B,Dobkin D P,Huhdanpaa H.The quickhull algorithm for convex hulls.ACM Transactions on Mathematical Software,1996;22(4):469-483
12 Chen M,Fang Y,Chen J.Influence of initial convex hull on the efficiency of quickhull algorithm.Science of Surveying and Mapping,2016;41(7):23-27
13 Anderson K R.Re-evaluation of an efficient algorithm for determining convex hull of a finite planar set.Information Processing Letters,1978;7(1):53-55
14 Gomes A J P.A total order heuristic-based convex hull algorithm for points in the plane.Computer-aided Design,2016;70:153-160
15刘崇,任立峰,史建伟,等.人体平衡能力的评价系统.中国组织工程研究与临床康复,2009;13(2):363-367Liu Chong,Ren Lifeng,Shi Jianwei,et al.Evaluation system of human balance ability.Journal of Clinical Rehabilitative Tissue Engineering Research,2009;13(2):363-367
16安美君,邹任玲,胡秀坊,等.人体重心动摇轨迹包络面积的快速算法.计算机工程,2011;37(10):255-256An Meijun,Zhou Renlin,Hu Xiufang,et al.Fast algorithm for envelope area of body barycenter swaying trajectory.Computer Engineering,2011;37(10):255-256
17 Andrew C C Yao.A Lower Bound to Finding Convex Hulls.Journal of the ACM,1981;28(4):780-787